Research on the Estimation of Locally Stationary and Related Processes

Abstract : The main objective of our research is the modeling, analysis, simulation and estimation of locally stationary signals, time series, data, images, etc. We have made an important advance in the statistical analysis of aerothermal data. We have shown that they fit very well into models of locally power law processes and we have estimated effectively and accurately the structure of the power and the log intercept. Our results are different from those previous analyses had produced and could have quite significant impact in our understanding of laser beam propagation in the atmosphere. The analytical and statistical methods that we use are of general interest and can be used in many other situations where local power law processes arise.